MonoForest Framework for Tree Ensemble Analysis

In this work a new structure for representing an ensemble of decision trees was proposed: instead of using a graph model, any tree was transformed into a well-known polynomial form. The new concept was applied to the tasks: theoretical analysis, model reduction (pruning) and interpretation. The polynomial shape of the ensemble of trees allows to directly interpret the original model. My experiments show comparable results with modern best interpretation methods. Another application of the new framework is the pruning of tree ensembles: you can drop monomials from the polynomial. Thus, you can reduce the size of the model up to 3 times. The equivalence of different forms of trees with the same polynomial was also shown. This fact makes it possible to interpret tree ensemble models in a new easy way. The problem of finding the optimal ensemble of trees with a fixed structure of the equivalent ensemble was also formulated and a greedy solution to this problem was proposed.